Write Nat/Unit/Empty/Id Eliminators Through NbE and Bidir Elaboration

2026-04-19 13:55:05 +00:00
parent a154e2b98c
commit 85be37b1d6
8 changed files with 374 additions and 2 deletions
@@ -11,6 +11,18 @@ inductive Raw where
  | pair : Raw → Raw → Raw
  | fst  : Raw → Raw
  | snd  : Raw → Raw
+  | nat  : Raw
+  | zero : Raw
+  | succ : Raw → Raw
+  | natElim : Name → Raw → Raw → Name → Name → Raw → Raw → Raw
+  | unit : Raw
+  | triv : Raw
+  | unitElim : Name → Raw → Raw → Raw → Raw
+  | empty : Raw
+  | emptyElim : Name → Raw → Raw → Raw
+  | id   : Raw → Raw → Raw → Raw
+  | refl : Raw
+  | idElim : Name → Name → Raw → Raw → Raw → Raw → Raw
  | univ : Nat → Raw
  | letE : Name → Raw → Raw → Raw → Raw
  | ann  : Raw → Raw → Raw
@@ -25,6 +37,18 @@ inductive Tm where
  | pair : Tm → Tm → Tm
  | fst  : Tm → Tm
  | snd  : Tm → Tm
+  | nat  : Tm
+  | zero : Tm
+  | succ : Tm → Tm
+  | natElim : Tm → Tm → Tm → Tm → Tm
+  | unit : Tm
+  | triv : Tm
+  | unitElim : Tm → Tm → Tm → Tm
+  | empty : Tm
+  | emptyElim : Tm → Tm → Tm
+  | id   : Tm → Tm → Tm → Tm
+  | refl : Tm
+  | idElim : Tm → Tm → Tm → Tm → Tm
  | univ : Nat → Tm
  | letE : Tm → Tm → Tm → Tm
  deriving Repr, Inhabited, BEq, DecidableEq